Biden appeared at a ceremonial swearing-in for Latino lawmakers sponsored by the Congressional Hispanic Caucus Institute (CHCI) in Washington, D.C. A record 36 Latino members will serve in the House and Senate in this upcoming Congress.

Despite potential impediments facing immigration reform, Biden claimed that a consensus has begun to build around the issue.

"In one sense, we have a long way to go, bringing 11 million Hispanics out of the shadows and into the light of day," he said. "What's different today is that the rest of the nation, the rest of America, recognizes it's time. It's your time."

Biden also sought to reassure skeptics on the administration's willingness to tackle a big issue like immigration after a bruising fight over the so-called "fiscal cliff."

Partisan rancor defined the fiscal cliff debate, and is likely to reemerge around pressing budget issues in the next few months. But Biden said that Republicans have begun to change their tune on immigration following an election in which more than seven in ten Latino voters backed President Obama over GOP candidate Mitt Romney.

"Have you ever seen a time when the Republicans had a more rapid epiphany about immigration than the one they had in this past election? All of the sudden -- we've got a lot more work to do -- but the point is the American people know what their leaders are only figuring out, the awesome potential [of the Latino community]," Biden said.

Referencing the results of the election, the vice president said Latino voters are "the center of our nation's future."

"If you ignore the needs of the Hispanic people, you will not win," Biden added.

Still, some advocates fear that impending showdowns over issues like the debt limit and the "sequester" spending cuts could take attention away from addressing immigration reform -- a major Obama campaign promise dating from his first run for office. And far from all Republicans have signed on to a comprehensive immigration reform package that includes a pathway to citizenship, which the White House supports.

The White House was quick to tamp down concerns after a deal on the fiscal cliff was reached. White House officials told The Huffington Post on Wednesday that its plan to move ahead on immigration this month would proceed.

Speaking about immigration, gun control and other second-term agenda items, Obama told reporters just after a deal was reached on Tuesday that, "it's not just possible to do these things; it's an obligation to ourselves and future generations."